Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model

Giesselmann, Jan and Pryer, Tristan (2013) Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model. (Submitted)

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Abstract

We design consistent discontinuous Galerkin finite element schemes for the approximation of a quasi-incompressible two phase flow model of Allen--Cahn/Cahn--Hilliard/Navier--Stokes--Korteweg type which allows for phase transitions. We show that the scheme is mass conservative and monotonically energy dissipative. In this case the dissipation is isolated to discrete equivalents of those effects already causing dissipation on the continuous level, that is, there is no artificial numerical dissipation added into the scheme. In this sense the methods are consistent with the energy dissipation of the continuous PDE system.

Item Type: Article
Uncontrolled Keywords: Quasi-incompressibility, Allen--Cahn, Cahn--Hilliard, Navier--Stokes--Korteweg, phase transition, energy consistent/mimetic, discontinuous Galerkin finite element method.
Subjects: Q Science > QA Mathematics
Depositing User: Dr Jan Giesselmann
Date Deposited: 05 Aug 2013 07:04
Last Modified: 22 Sep 2017 09:43
URI: http://preprints.acmac.uoc.gr/id/eprint/238

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